Body Deformates In Weird Ways When Bone is Rotated
From your Screenshot i can tell that a lot of vertices are assigned to the Vertex group/Bone from the lower arm (or the corresponding hand/fingers). You should be able to see this influence if you go into Weight Paint mode and select those bones.

First I recommend going into wireframe mode and selecting every face you know, shouldn't be influenced by these bones at all. Then hit "Remove" for the Vertex Groups of the Bones in the corresponding lower Arm and Hand. This way those Bones won't effect Areas they aren't supposed to.



After that you'll have to balance the influence from the upper and lower arm in Weight Paint Mode, so it bends in a natural way.